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Instructor: Akos Lada Harvard Kennedy School Mid-Career MPA Summer Program 2014 Problem/Question of the Day Distributed: 7/21/14 Due in Class: 7/22/14 1. Consider the market for economics textbooks (You don’t have to worry about whether the prices and quantities are reasonable). Let qD = 40-0.5P represent the demand curve for an individual consumer, and qS = -80+4P represent the supply curve for an individual producer. Furthermore, assume that there are 100 identical consumers and 5 identical producers in the market. The quantity units are books and the currency is US dollars. a. Plot the individual consumer demand curve and individual firm supply curve on separate graphs. (Graphs do not have to be to scale or on graph paper, but please label the important features- intercepts, etc.) b. What are the equations for the market supply and demand curves? Please plot market demand and supply on the same graph. How do these curves compare to those for individual supply and demand? Because all of the individuals are identical, if one individual demands qD books, then 100 people demand 100*qD books. Multiplying the right hand side of our individual demand equation by 100, we get: QD = 4000-50P. For firms, since they are also identical, if one firm supplies qS books then 5 firms supply 5* qS books. Thus, we get: QS = -400+20P. You can also think of this as horizontal addition... You should get this graph: Instructor: Akos Lada Harvard Kennedy School Mid-Career MPA Summer Program 2014 As for how these compare to individual supply and demand, the graphs for market supply and demand are stretched horizontally, i.e. along the quantity axis. The P-axis intercepts stay the same, but the slope of the lines is different. c. What is the equilibrium price and quantity in the market for books? To solve here we need to set QS=QD - using the equations we solved for above we have: QD = 4000-50P and QS = -400+20P So 4000-50P=-400+20P --> 4400=70P --> P=440/7, so price is $62.86 USD. To find quantity we can just plug this P value back into wither of the two quantity expressions: QD = 4000 - 50(440/7) = 4000-3143 = 857 books So P = $6,286 and Q = 857 books in equilibrium. d. If an individual’s income rises, will he demand more or fewer books? What assumption (in economic terms) did you make to reach this conclusion? He will likely demand more books. The assumption that I made was that books are a normal good, in which case demand goes up as income rises. You could also argue that books are inferior goods, in which case the opposite would be true (less income would lead to a greater demand), because the individual does not want to learn more economics but consumes income in other (better?) ways. It’s a bit of a judgment call. e. If the price of hardcover fiction books falls, what happens to the demand for paperback fiction books? Why? If the price of electricity rises, what happens to demand for books? Why? Instructor: Akos Lada Harvard Kennedy School Mid-Career MPA Summer Program 2014 If the price of hardcovers falls, the demand for paperbacks decreases. This is because the two are substitutes, so as the price of hardcovers goes down the demand for paperbacks goes down too. If the price of electricity rises, the demand for paperback is (virtually) unchanged, since they are unrelated goods. (You could argue that if demand for electricity is very inelastic, there would be less money left over for other goods, but this is a minor effect. Or that people read by electric light. On the other hand, maybe consumers use their TV less and read instead. The important point is that electricity and paperbacks are considered neither substitutes nor complements.) f. Suppose that the fiction writers’ union recently negotiated higher wages. What happens to the supply of paperbacks? Explain. Wages are an input price. Input prices are a determinant of supply, and when input prices go up, supply goes down. Therefore the supply of books goes down (decreases). g. Now suppose that consumer groups lobbied the government to pass a bill to keep the price of paperbacks lower than the equilibrium price. What type of price control would they want to lobby for? What would result, economically speaking, from such a price control if it was passed and enforced? They would want a price ceiling set below the market equilibrium price. However, such a binding price ceiling would lead to excess demand and insufficient supply - in other words, a shortage. h. Suppose the price control in part (g) was passed at a price of $50. What would be the resulting price and quantity consumed in the market? What would be the amount of shortage/surplus? With a price ceiling of $50, the quantity demanded and supplied would be: QD = 4000-50P with P=50, so QD = 1500 QS = -400+20P with P=50, so QS = 600 So we can see here that there is a shortage, as expected. 1500 books are demanded but only 600 are supplied. There is a shortage of 900 books. The market price would be $50 and the market quantity would be 600 books.